A fine dish for lunch or dinner. Accompany with broccoli, peas, or another green vegetable.
Put the chicken into a stockpot and add cold water to cover. Add the bay leaf, carrots, garlic, onions, and peppercorns. Cover the pot, raise the heat to medium high, and bring it to a boil. Reduce the heat and simmer for 30 minutes, or until the chicken is tender. Remove the chicken, separate the meat from the skin and bones, and chop it. Discard the skin and bones. Strain the stock and reserve.
Preheat the oven to 425°F. Grease a 2-quart casserole. In a large saucepan over medium heat, melt the butter. Add the mushrooms and green pepper and sauté until the vegetables are soft. Sprinkle with the flour and tarragon and stir to blend. Add 2 cups of the reserved stock and stir until smooth. Slowly add the cream and stir until blended. Season with salt and pepper. Add the cheese and stir until it melts. Spread the chopped chicken in the bottom of the casserole. Top with a layer of rice and then a layer of sauce. Repeat, ending with the sauce. Bake for 30 minutes, or until bubbling.